Assassin's Creed 4: Black Flag Walkthrough Part 12 – Sequence 3: "Prizes and Plunder"

Full Synchronization:
Use the swivel gun to kill 3 sailors
Plunder 20 rum

Start this mission and then let it run a while before turning it in. For now, it is consequence free to go pirating and ransacking goods. Use the spy glass when prompted and find a ship. Look at its cargo then move on. Fire off whatever guns are available when you get close  For schooners, it does not take much to drop them into the red portion of their health.

Once they hit the red, immediately get over there. Alternatively, you can head to the swivel gun and shoot down the specific number for the take over. Otherwise, just head over there and kill that many of their crew. Once done, you will find you can collect the cargo of the taken ship and use it to repair the Jackdaw.

After you take your first ship, you will be prompted to head to Salt Key. It is recommended that you instead take some time to hunt and plunder a number of ships. Until the end of the next mission, piracy carries no penalty. Be sure to take some time to loot a total of 30 sugar. This will make the next mission a lot easier to get Full Synchronization on. Just steady make your way to Salt Key, looting all the way. The more looted now, the better.